LG Problem Set #1: Game #11

[smile22]

Hello,

I have a question on game #11 that is located in the LG problem set #1 packet. According to the packet, the game comes from the June 1996 exam. The game is regarding two boats and the assignment of 8 people (three adults and five children). I am having some difficulty in this problem and how to properly set it up. Any input that you can provide would be greatly appreciated.


Thank you!

[Jason Schultz]

Hi Smile22,

This is a balanced, defined grouping game where you are creating two groups of 4 from 8 people. Note however, that the first rule requires at least one adult in each boat, so you are limited to only one distribution: 2 Adults and 1 Kid in one of the boats, 1 Adult and 3 Kids in the other.

2) Is a straightforward conditional rule. F2 -> G2. And any conditional rule also brings the contrapositive: Not G2 -> Not F2. Since there are only two possibilities, you can also picture this as G1 -> F1. Note that if F and G are in the same boat, H has to be in the other.

3) Same as 2. V1 -> W2, with the contrapositive Not W2 -> Not V1. W1 -> V2

4) A "double-not" rule, which leaves you with X <-/-> Z

So you have 4 seats to fill in each boat, but one of them in each boat is set aside for the X/Z double not group.

Try that out.

[smile22]

Thank you for the response. I will try this out and rework the problem. Thanks again for your help!

[emigini]

Hello,

I'm having trouble with the V1 W2 conditional. Wouldn't that make #17 impossible? (17 is essentially, "If V and W are assigned to the same boat, which pair must be in the same boat together?")

Thanks.

[KelseyWoods]

Hi emigini,

Thanks for your question!

The rule states that if V is in boat 1, then W is in boat 2. You correctly diagrammed that as:

V1 W2

The contrapositive would be:

W1 V2

This rule tells us that V and W cannot be together in boat 1. But what if V and W are in boat 2? W2 and V2 are necessary conditions in our contrapositive pair, so they don't have arrows leading away from them. This means we don't know anything else that must be true from satisfying the necessary conditions.

In general, when you have a contrapositive pair, you cannot have the two sufficient conditions (V1 & W1) together but you could have the two necessary conditions (W2 & V2) together. So for question 17, if V and W are assigned to the same boat as each other, that means they have to be in boat 2.

Hope this helps!

Best,
Kelsey